Radians to Degrees, Minutes, Seconds

[mathdad]

Reduce the following numbers of radians to degrees, minutes, and seconds.

(a). 0.47623.

(b). 0.25412.

Can someone work out (a) in steps? I can then use it as a guide to solve (b).

 

[MarkFL]

Okay, here is how I would work a):

First, let's get a decimal approximation for the number of degrees, with a good amount of precision:

$$0.47623\cdot\frac{180^{\circ}}{\pi}=\frac{85.7214}{\pi}^{\circ}\approx27.285969077515198^{\circ}$$

Okay, now we think of this as:

$$0.47623\approx27^{\circ}+0.285969077515198^{\circ}\cdot\frac{60'}{1^{\circ}}\approx27^{\circ}+17.15814465091188'$$

Continuing:

$$0.47623\approx27^{\circ}+17' + 0.15814465091188'\cdot\frac{60''}{1'}\approx27^{\circ}+17'+9.4886790547128''$$

Using standard notation and rounding some, we may write:

$$0.47623\approx27^{\circ}17'9.49''$$

 

[mathdad]

Okay, here is how I would work a):

First, let's get a decimal approximation for the number of degrees, with a good amount of precision:

$$0.47623\cdot\frac{180^{\circ}}{\pi}=\frac{85.7214}{\pi}^{\circ}\approx27.285969077515198^{\circ}$$

Okay, now we think of this as:

$$0.47623\approx27^{\circ}+0.285969077515198^{\circ}\cdot\frac{60'}{1^{\circ}}\approx27^{\circ}+17.15814465091188'$$

Continuing:

$$0.47623\approx27^{\circ}+17' + 0.15814465091188'\cdot\frac{60''}{1'}\approx27^{\circ}+17'+9.4886790547128''$$

Using standard notation and rounding some, we may write:

$$0.47623\approx27^{\circ}17'9.49''$$

There's got to be an easier way to do this, right?

 

[MarkFL]

There's got to be an easier way to do this, right?

There could be, but that's the most straightforward way I know to do such a conversion by hand (i.e. without using a calculator programmed to do such conversions).

 

[mathdad]

There could be, but that's the most straightforward way I know to do such a conversion by hand (i.e. without using a calculator programmed to do such conversions).

I recall watching a high school teacher on youtube.com using a totally different method.